Fix Docker production build: move tsx to dependencies, reinstall in production stage

The production Docker stage was copying pnpm symlinks between stages
which broke module resolution. Now does a fresh pnpm install --prod
in the production stage and runs from the server working directory.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

apps/server/package.json

@@ -19,13 +19,13 @@
     "drizzle-orm": "^0.44.2",
     "hono": "^4.7.10",
     "postgres": "^3.4.7",
+    "tsx": "^4.19.4",
     "uuid": "^11.1.0"
   },
   "devDependencies": {
     "@ai-tycoon/tsconfig": "workspace:*",
     "@types/node": "^25.6.0",
     "drizzle-kit": "^0.31.1",
-    "tsx": "^4.19.4",
     "typescript": "^5.8.3"
   }
 }